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Title
Number Machine 

Problem Statement
I have a "number machine" that always affects in the same way whatever number I put in it. For example, when I put in 1, the machine gives me 6; when I put in 3, it gives me10; when I put in 6, it gives me 16; and when I put in 9, it gives me 22. What will the machine give me if I put in 100?

 

Plans to Solve/Investigate the Problem

I plan to make a function chart and look for a pattern.

 

Investigation/Exploration of the Problem

 

0

1

3

6

9

 

6

10

16

22

 If we remove the (1,6) we will have:

 

0

3

6

9

 

10

16

22

 

The constant difference on the top row is 3 and the constant difference on the bottom row is 6. Looking at the ratio of the change in y to the change in x the slope of my linear equation would be 2. Next, I worked backwards to determine the y value when x =0 to be 4. The linear equation is y = 2x + 4.

 

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Author & Contact.
Dottie Mitcham

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